URBDP 591 A Lecture 11: Sampling and External Validity Objectives What is sampling? Types of Sampling –Probability sampling –Non-probability sampling External Validity

What is sampling? Is the process of selecting part of a larger group of participants with the intent of generalizing the results from the smaller group, called the sample, to the population. If we are to make valid inferences about the population, we must select the sample so that it is representative of the total population.

Why sampling? It is not possible to collect data about every member of a population since the population is often too large. Time, cost and effort constraints do not allow for collection of data about every member of a population. It is NOT necessary to collect data about all members of a population because valid and reliable generalizations can be made about a population from a sample using inferential statistics.

Sampling Definitions Universe: Theoretical and hypothetical aggregation of all elements in a survey. Eg, Americans. Population: A more specified theoretical aggregation. Eg, Adult Americans in spring Target Population: The population to which the researcher would like to generalize his or her results. Sampling Frame: Actual list of units from which the sample is drawn. Sample: A subset of the target population chosen so as to be representative of that population. Sampling Unit:: Elements or set of elements considered for sampling. Eg, persons, geographical clusters, churches.

Sampling Definitions

Sampling stages Identify the target Population Determine the sampling frame Select a sampling procedure Determine the sample size Select actual sampling units Collect data from respondents Information for decision-making Deal with nonresponse Reconcile frame & population

Types of Sampling Probability sampling: involves the selection of participants in a way that it is not biased. Every participant or element of the population has a known probability of being chosen to be a member of the sample. Nonprobability sampling: there is no way of estimating the probability that each participant has of being included in the sample. Therefore bias is usually introduced.

Probability Sampling When probability sampling is used, inferential statistics enables researchers to estimate the extent to which results from the sample are likely to differ from what we would have found by studying the entire population. - Simple random sampling - Systematic random sampling - Stratified random sampling - Cluster random sampling

Probability sampling methods are those in which the chance that a case is selected is known in advance. Cases are selected by chance, and therefor there is no systematic bias in the characteristics of the sample. Even without systematic bias in the way in which a sample is selected, the sample will still be subject to sampling error due to chance (recall that if you flip a coin 10 times you expect to get about 5 heads, but there's always a chance that you'll get very few or very many heads). In general, the amount of sampling error is due to the size of the sample (the larger the sample, the less sampling error) and the homogeneity of the population (if every case is the same, you will not get any sampling error). Probability Sampling Methods

Simple Random - Each member in the sampling frame has an equal probability of being selected. Systematic - Every kth member in the sampling frame is chosen. Stratified - Members in the sampling frame are grouped by forming classes or strata, thereafter selecting a simple random sample from EACH class or stratum. Cluster - Members in the sampling frame are grouped by forming classes or strata, thereafter simply electing to study all or a sample of members of only some (BUT NOT ALL) of the classes or stratum. Probability Sampling

A simple random sample (SRS) is one in which cases are selected from the population based strictly on chance, and in which the probability of selection is the same for every case in the population. If there are N cases in the sampling frame (i.e., the population) and n cases are to be selected for the sample, then every case has an n/N chance of being selected. Simple random sampling is the most straightforward probability sampling techniques, but it does not work well for all research purposes. For example, imagine that you want to compare Native Americans and Whites in terms of some attribute. If you construct an SRS of 500 people, will you get enough Native Americans in the sample? A simple random sample (SRS)

Homogeneity and Heterogeneity Homogeneous: Having few differences. –Example: A group of 30-year-old male USA second-year university students majoring in Sociology is a homogeneous group. Heterogeneous: Having many differences. –Example: A group of international students.

Stratified Sampling Increases efficiency by limiting population variance or increasing sampling accuracy Stratifying (grouping) variable such that –it is strongly associated with the key dependent variable –each group is more homogeneous than the population in terms of the key dependent variable Sample size for each stratum will depend on –variance in the stratum –relative cost of sampling from the stratum Proportional (to size)stratified sampling Disproportional stratified sampling

Cluster Sampling Increases efficiency by reducing cost 2 step process –form clusters (each cluster is as heterogeneous as the population) –randomly select some clusters (probability proportional to size), collect data from all elements of the selected clusters Often used in area sampling

Stratified vs. Cluster sampling: Stratified: –Subgroups defined by variables under study. –Strive for homogeneity within subgroups, heterogeneity between subgroups. –Randomly choose elements from within each subgroup. Cluster: –Subgroups defined by ease of data collection. –Strive for hetero- geneity within subgroups, homo- geneity between subgroups. –Randomly choose a number of subgroups, which we study in their entirety.

Area sampling A variety of cluster sampling based on location, or area. Example: Is there a market for a new grocery store in Wallingford? Procedure: Identify a group of housing estates around the proposed location. This is the area. Randomly sample estates within that area. These are the clusters.

Nonprobability Sampling the probability of any population element being selected for the sample is not known a priori: –convenience sampling –judgement sampling –quota sampling –snowball sampling

Convenience Sampling Collecting data from people who are conveniently available. Example: Customers walking by in a mall.

Judgment Sampling Purposely choosing subjects who are best able to provide the information required. Example: Asking senior planners about the implementation of comprehensive plans.

Quota Sampling Nonprobabilistic attempt to get representation of major sub-groups in the sample sub-groups usually defined in terms of easily identifiable demographics may match marginal frequencies but difficult to match joint frequencies selection of quota basis should have a relationship with the variable of interest similar to stratified sampling, but different –quota sampling is judgement or convenience based and not probabilistic

Snowball sampling involves interviewing or observing one member of a population, and then asking that person to identify other people who might be included in the sample. This technique is especially useful for interviewing people who are hard to find or hard to identify, and who are somehow interconnected. Snowball Sampling

Generalizability and Statistics Results with non-probability samples are USUALLY not generalizable. If generalizability is not required, then neither are statistical tests of significance! Important point: If the sample doesn’t represent the population, then statistical tests are NOT NECESSARY and may be misleading.

Sample Size The larger the sample size, the higher the confidence (smaller values of p) The larger the variance (difference amongst subjects), the lower the confidence. Larger variance requires a larger sample size to achieve the same level of confidence.

Sample Size We can easily determine the minimum sample size needed to estimate a process parameter, such as the population mean. When sample data is collected and the sample mean is calculated, that sample mean is typically different from the population mean x. This difference between the sample and population means can be thought of as an error. The margin of error E is the maximum difference between the observed sample mean  and the true value of the population mean : Rearranging this formula, we can solve for the sample size necessary to produce results accurate to a specified confidence and margin of error

External validity The extent to which the results obtained in a given study would also be obtained for different participants and under different circumstances (real world) Dependent upon sampling procedure Improve primarily by replication under different conditions.

Population validity. To what population can you generalize the results of the study? This will depend on the makeup of the people in your sample and how they were chosen. If you have used young, white middle class, above average intelligence, Western students as your subjects, can you really say your results apply to all people? Ecological validity. Laboratory studies are necessarily artificial. Many variables are controlled and the situation is contrived. A study has higher ecological validity if it generalizes beyond the laboratory to more realistic field settings. Threats to external validity

External Validity LowMediumHigh Actual Sample unrepresentative of the population Some attempt to obtain good sample Actual sample representative of the population POPULATION - Representativeness of accessible population - Adequacy of sampling method - Adequacy of response rate ECOLOGY Naturalness of setting or conditions Adequacy of rapport with observer Naturalness of procedures or tasks Appropriateness of timing Unnatural setting, tester, procedure, time Somehow artificial setting, tester, procedure, time Unnatural setting, tester, procedure, time

Target Population Accessible Population or Sampling Frame Selected Sample N = 100 Sampling Design Assignment Design Actual Sample N = 75 Group 1 N = 25 Group 2 N = 25 Group 3 N = 25 External Validity depend on sampling design High: Probability sampling e.g. simple random sample Low: Non probability sampling e.g. quota sampling Internal Validity how experiment is controlled and groups are assigned High: Random assignment Low: Existing groups or selfselection